2.1 Introduction to Newton-Raphson Method

Methods such as the bisection method and the false position method of finding roots of a nonlinear equation \(f(x)=0\) require bracketing of the root by two guesses. Such methods are called bracketing methods. These methods are always convergent since they are based on reducing the interval between the two guesses so as to zero in on the root of the equation. In the Newton-Raphson method, the root is not bracketed. In fact, only one initial guess of the root is needed to get the iterative process started to find the root of an equation. The method hence falls in the category of open methods. Convergence in open methods is not guaranteed, but it does so much faster than the bracketing methods if the method does converge.